Bruhn, whose real name was Bolton Evers, entered the school of the Royal Danish Ballet in 1937, became a member of the company in 1947, and was promoted to principal dancer in 1949. His career as an international solo dancer began in 1947 and in 1956 he resigned from the Royal Theatre and toured the world. He was chief of the Royal Opera Ballet, Stockholm (1967-1971), then the National Ballet of Canada (1983-86).

In 1961, shortly after defecting from Soviet Union, Rudolf Nurejev arranged a meeting with Bruhn in Copenhagen. They met in the bar of the Hotel d'Angleterre, which at the time was a meeting place for Copenhagen gay peple. Thus began a life long relationship between Erick and "Rufik". Nureyev moved in with Bruhn, who lived in Copenhagen with his mother. A year later they moved together to a flat in London where both were guests dancers at the Royal ballet.

In the longer run Bruhn could not cope with Nureyev's closeness and promiscuity. He tried to withdraw from the relationship, but Nureyev followed him wherever he went. Their sexual relationship ended in 1967. Mutual attraction had turned into jealousy. Their friendship, however, lasted. Nureyev was present at Bruhn's deathbed in Toronto in 1986.